What quantity of heat is needed to convert 1kg of ice at -10C to liquid at 20C?
add the following heats:
heat to change ice at -10 to 0C
heat to melt ice at 0C
heat to heat water from 0C to 20C
To calculate the quantity of heat needed to convert ice at -10°C to liquid at 20°C, we need to consider two steps:
Step 1: Heating the ice from -10°C to 0°C
Step 2: Melting the ice at 0°C to liquid at 0°C
Step 3: Heating the liquid from 0°C to 20°C
Let's calculate the heat required for each step.
Step 1: Heating the ice from -10°C to 0°C
The specific heat capacity of ice is 2.09 J/g°C.
The specific heat capacity of water is 4.18 J/g°C.
ΔQ1 = mass * specific heat capacity * ΔT
ΔQ1 = 1 kg * 2.09 J/g°C * (0°C - (-10°C))
ΔQ1 = 1 kg * 2.09 J/g°C * 10°C
ΔQ1 = 20.9 kJ
Step 2: Melting the ice at 0°C to liquid at 0°C
The heat required for melting (latent heat) for ice is 334 kJ/kg.
ΔQ2 = mass * latent heat
ΔQ2 = 1 kg * 334 kJ/kg
ΔQ2 = 334 kJ
Step 3: Heating the liquid from 0°C to 20°C
ΔQ3 = mass * specific heat capacity * ΔT
ΔQ3 = 1 kg * 4.18 J/g°C * (20°C - 0°C)
ΔQ3 = 1 kg * 4.18 J/g°C * 20°C
ΔQ3 = 83.6 kJ
The total heat required is the sum of the heat required for each step:
Total heat = ΔQ1 + ΔQ2 + ΔQ3
Total heat = 20.9 kJ + 334 kJ + 83.6 kJ
Total heat = 438.5 kJ
Therefore, approximately 438.5 kJ of heat is needed to convert 1 kg of ice at -10°C to liquid at 20°C.
To find the quantity of heat required to convert 1kg of ice at -10°C to liquid at 20°C, we need to consider two distinct processes:
1. Heating the ice from -10°C to 0°C: We need to find the heat required to raise the temperature of ice from its initial state (-10°C) to its melting point (0°C).
2. Melting the ice: Once the ice has reached 0°C, we need to determine the heat required to completely melt it into liquid water.
3. Heating the water from 0°C to 20°C: Lastly, we need to calculate the heat needed to raise the temperature of the liquid water from 0°C to the desired final temperature (20°C).
Now, let's break down each step to calculate the total heat required:
1. Heating the ice from -10°C to 0°C:
The specific heat capacity of ice is approximately 2.09 J/g°C. Since we have 1kg of ice, we multiply the mass by the specific heat capacity and the temperature change:
Heat = mass × specific heat capacity × temperature change
= 1kg × 2.09 J/(g°C) × (0°C - (-10°C))
= 1kg × 2.09 J/(g°C) × 10°C
= 20.9 kJ
Therefore, it requires 20.9 kJ of heat to raise the temperature of 1kg of ice from -10°C to 0°C.
2. Melting the ice:
To calculate the heat needed to melt the ice, we use the latent heat of fusion, which is approximately 334 kJ/kg for water. As we have 1kg of ice:
Heat = mass × latent heat of fusion
= 1kg × 334 kJ/kg
= 334 kJ
Hence, it requires an additional 334 kJ of heat to completely melt 1kg of ice into liquid water.
3. Heating the water from 0°C to 20°C:
The specific heat capacity of water is approximately 4.18 J/g°C. As we have 1kg of water, we multiply the mass by the specific heat capacity and the temperature change:
Heat = mass × specific heat capacity × temperature change
= 1kg × 4.18 J/(g°C) × (20°C - 0°C)
= 1kg × 4.18 J/(g°C) × 20°C
= 83.6 kJ
Thus, it requires 83.6 kJ of heat to raise the temperature of 1kg of water from 0°C to 20°C.
To find the total quantity of heat required, we sum up the heat required in each step:
Total heat = Heat for heating ice + Heat for melting ice + Heat for heating water
= 20.9 kJ + 334 kJ + 83.6 kJ
= 438.5 kJ
Therefore, it requires a total of 438.5 kJ of heat to convert 1kg of ice at -10°C to liquid at 20°C.